Jonathan L. Verner
Lonely points revisited

Comment.Math.Univ.Carolin. 54,1 (2013) 105-110.

Abstract:In our previous paper, we introduced the notion of a lonely point, due to P.~Simon. A~point $p\in X$ is lonely if it is a limit point of a countable dense-in-itself set, it is not a limit point of a countable discrete set and all countable sets whose limit point it is form a filter. We use the space ${\mathcal G}_\omega$ from a paper of A.~Dow, A.V.~Gubbi and A.~Szyma\'nski [{\it Rigid Stone spaces within ZFC\/}, Proc. Amer. Math. Soc. {\bf 102} (1988), no.~3, 745--748] to construct lonely points in $\omega^*$. This answers the question of P.~Simon posed in our paper {\it Lonely points in $\omega^*$\/}, Topology Appl. {\bf 155} (2008), no.~16, 1766--1771.

Keywords: $\beta\omega$, lonely point, weak P-point, irresolvable spaces
AMS Subject Classification: 54D80 54D40 54G05